Radio astronomy is undergoing a renaissance, as the next generation of instruments provides a massive leap forward in collecting area and therefore raw sensitivity. However, to achieve this theoretical level of sensitivity in the science data products, we need to address the much more pernicious systematic effects, which are the true limitation. These become all the more significant when we consider that much of the time used by survey instruments, such as the Square Kilometre Array (SKA), will be dedicated to deep surveys. CHILES is a deep H I survey of the COSMOS field, with 1000 hr of Very Large Array time. We present our approach for creating the image cubes from the first epoch, with discussions of the methods and quantification of the data quality from 946 to 1420 MHz-a redshift range of 0.5-0. We lay out the problems we had to solve and describe how we tackled them. These are important because CHILES is the first deep wide-band multiepoch H I survey and has relevance for ongoing and future surveys. We focus on the accumulated systematic errors in the imaging, as the goal is to deliver a high-fidelity image that is only limited by the random thermal errors. To understand and correct these systematic effects, we ideally manage them in the domain in which they arise, and that is predominately the visibility domain. CHILES is a perfect test bed for many of the issues we can expect for deep imaging with the SKA or ngVLA, and we discuss the lessons we have learned.